Math.Net Monotone Cubic Fits over an interval

Background

NIST:  constraints for cubic monotonicity
monpol: Monotone Polynomials (in R)

By observation, Cubic is monotonic if

• end slopes are 0 or of the same sign
• inflection point in interval is 0 or of the same sign

cubic:  y = a + b*x +c*x*x + d*x*x*x;   0 <= x <=1

cubic slope:   b + 2*c*x + 3*d*x*x

slope @0:   b

slope @1:   b + 2*c + 3*d

non-negative monotone end slopes product

b*(b + 2*c + 3*d) >= 0

inflection point:   2*c + 6*d*x = 0

x = - c/3*d

slope must must be checked for 0 > c/3*d > -1

Math.Net.Fit.Curve() interative optimization

based on FindMinimum.OfScalarFunction

Implement a cubic function, constraining optimized coefficients

by returning full scale values for non-monotonic slopes.

• Math.Net.Fit.Curve uses NelderMeadSimplex
• Math.Net NelderMeadSimplex Example